Chapter 2: Propagation of electromagnetic wavesIntroductionWhen studying dynamic electromagnetic fields, we usually
start with the propagation of waves in an infinite homogeneous medium, which is supposed being linear and isotropic.
In this situation, a single wave is propagating, which can be attenuated only is lossy
medium is assumed.
Electromagnetic waves, which propagate in infinite
homogeneous medium, can be classified according to their
equiphase surface
as planar, cylindrical and spherical.
Plane waves can be observed in a long distance from
the transmitting antenna. Plane wave propagation can be mathematically described by
a scalar differential equation in the
Cartesian coordinate system.
Cylindrical wave propagates from an infinitely long
direct wire, which is flown by a highfrequency current. Cylindrical wave propagation
is described by a scalar differential equation in the cylindrical coordinate system.
Spherical wave propagates from a point source. Spherical
wave propagation is described by a vector differential equation in the spherical
coordinate system.
Propagation of the abovedescribed waves is relatively
wellunderstandable and wellimaginable. Even the mathematical relations describing
propagation of those waves are relatively simple, and moreover, the final equations are
of a closed form (i.e., we get relatively simple formulae which can be easily used for
practical calculations). Therefore, those topics are not discussed in our electronic
textbook.
Theoretical description of wave propagation in homogeneous
medium is given in [1]
and [2].
Practical relations for the solution of given engineering tasks are in
[3] at your disposal.
Examination of electromagnetic wave propagation complicates
in the situation when some inhomogeneity appears in the medium. The inhomogeneity can cause
wave reflection,
wave scattering
or wave diffraction.
Reflected (scattered, diffracted) waves interfere with incident waves. In the surrounding of the inhomogeneity, regions with higher intensity (compared to the case without inhomogeneity) can appear
(primary wave and secondary one are of the same phase). Next, regions
with very low intensity can be found (primary wave and secondary one are
of the opposite phase).
Therefore, computation of the wave propagation in an
inhomogeneous medium is much more complicated than is a homogeneous one, and even understanding
the mathematical description and building a proper notion is much harder. Therefore, we are
going to study the related phenomena more in detail here.
In an inhomogeneous medium, its electric and magnetic parameters
(permittivity, conductivity, permeability) change from a region to another region. Moreover,
variations of parameters can be continuous or discontinuous.
The discontinuous variation of parameters is characteristic
for the surface of objects, i.e. for an medium containing conductive or dielectric
(or ferromagnetic) objects. In a real situation, buildings, trees, hills, cars, people
or raindrops play the role of those objects. In our textbook, we start to examine those
phenomena in an example of a thin planar sheet, which neither reflects nor transmits
the incident wave. We are speaking about
Fresnel diffraction
and we describe it in chapter 2.1.
In the practical life, more realistic objects have to be considered.
Including those considerations to our computations is enabled by the
general theory of diffraction, which is described in
chapter 2.2.
In this chapter, the diffraction on an infinitely long perfectly conducting circular
cylinder is discussed.
In chapter 2.3,
geometric optics
is introduced. Geometric optics is an efficient method for the computation of wave
phenomena in more complicated media. This method adopted the conception of wave
propagation along beams. Comparing to the classical geometric optics, we can compute
the intensity variations and
wave polarization for wave propagation in the medium with
continuously changing parameters.
Chapter 2.4 deals with the
geometric theory of diffraction
(GTD). GDT extends the abilities of the geometric optics to the media with discontinuous inhomogeneities. GTD solves interaction of beams and objects, and laws of geometric optics are modified in order to eliminate obvious errors (intensity discontinuities on the border between the reflection and shade) on one hand,
and to preserve advantages of the geometric optics on the other hand (conception of beams).
All the section is closed by the examination of layered media (media consisting of several layers of different permittivity and different thickness).
Borders of layers are usually planar and parallel. Hence, the layered media consists of
a certain number of planparallel layers. More information is given in chapter 2.5.
